Rigorous numerics for localized patterns to the quintic swift-hohenberg equation

Yasuaki Hiraoka, Toshiyuki Ogawa

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Localized patterns of the quintic Swift-Hohenberg equation are studied by bifurcation analysis and rigorous numerics. First of all, fundamental bifurcation structures around the trivial solution are investigated by a weak nonlinear analysis based on the center manifold theory. Then bifurcation structures with large amplitude are studied on Galerkin approximated dynamical systems, and a relationship between snaky branch structures of saddle-node bifurcations and localized patterns is discussed. Finally, a topological numerical verification technique proves the existence of several localized patterns as an original infinite dimensional problem, which are beyond the local analysis.

Original languageEnglish
Pages (from-to)57-75
Number of pages19
JournalJapan Journal of Industrial and Applied Mathematics
Issue number1
Publication statusPublished - 2005 Feb


  • Conley index
  • Localized patterns
  • Quintic Swift-Hohenberg equation
  • Rigorous numerics
  • Snaky bifurcation structure

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics


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